Dispersion relations, time domain propagation, and Jahn-Teller effects in two-dimensional spectroscopy

Two-dimensional Fourier transform (2D FT) spectroscopy is a type of four-wave mixing experiment; three excitation fields interact with the sample, which radiates a fourth (signal) field. In this thesis, a model is constructed to investigate signatures of a conical intersection in 2D FT spectra. The model Hamiltonian is appropriate for a four-fold symmetric molecule. Its excited state is doubly-degenerate at the equilibrium geometry, but the degeneracy is lifted by Jahn-Teller active vibrations. In the weakly-coupled non-adiabatic limit, low-amplitude signatures of conical intersection dynamics in a 2D spectrum are present for excitation pulses with parallel polarizations. The model is then extended to include damped symmetric vibrations and asymmetric vibrations which cause permanent electronic dephasing. Jahn-Teller distortions mix the character of the excited electronic states; dephasing functions for asymmetric vibrations require information about paths through the states. The model relies on symmetry that remains after the perturbation is introduced to distinguish between the singly-excited electronic states so that their dephasing by asymmetric vibrations can be properly accounted for. For parallel excitation pulses in the weakly coupled non-adiabatic limit, asymmetric vibrations do not produce the same time domain decay of the signal in the echo-slice direction as they produce in the anisotropy.;This thesis also uses model spectra to investigate experimental time-domain distortions of 2D signals. Distortions resulting from propagation in collinear and non-collinear geometries affect causality and the validity of dispersion relations for the 2D spectra. Causality is closely connected to dispersion relations; violation of causality can interfere with the interconversion of real and imaginary parts of the spectrum. Representations of two-dimensional spectra can be non-causal, even for the collinear geometry. An experimentally accessible representation which minimizes absorptive and dispersive distortions and appears to be causal for collinear 2D spectra is recommended; dispersion relations hold surprisingly well for this representation. Non-collinear signals violate causality regardless of optical density and representation.